John Whittingdale said MPs wanted to determine whether social networks were "doing as much as they can" to protect users and identify perpetrators.

He spoke after a female MP and a feminist campaigner received threats of rape on Twitter.

Meanwhile, police say a second man has been arrested on suspicion of harassment in connection with the case.

This latest debate over internet "trolls" - those who use their social media accounts to abuse others - erupted when Caroline Criado-Perez was bombarded with abuse via Twitter after successfully campaigning to have author Jane Austen depicted on the new £10 note.

She told BBC Two's Newsnight: "The threats have been so explicit and so graphic that they've sort of stuck with me in my head and have really put me in fear."

She said she hoped her case had been "a wake-up call for Twitter", adding: "It will hopefully have led them to realise that they are not equipped to deal with this kind of thing properly."

Scotland Yard says a 25-year-old man from South Shields has been arrested on suspicion harassment of Ms Criado-Perez and MP Stella Creasy.

Media captionDel Harvey, Head of Trust and Safety at Twitter: "I don't want people to think we're not taking this seriously"

Northumbria Police say they took the action after Newsnight traced threatening Twitter messages to accounts in the town.

Earlier, a 21-year-old man arrested on suspicion of harassment offences was bailed until a date in mid-September.

'Greater urgency'

A number of women who spoke out in support of Ms Criado-Perez were subsequently targeted in a similar way, including Ms Creasy, the MP for Walthamstow.

She reported the barrage of abuse to the Metropolitan Police on Monday night, and Scotland Yard said later it was considering an allegation of "malicious communications".

The Commons culture committee was already planning to hold an inquiry in the autumn into harmful online content and child protection.

I hope that Twitter have seen the strength of public opinion that exists in Britain at the momentJohn Whittingdale MP, Culture committee chairman

Mr Whittingdale said that, as part of that, the MPs would want to speak to social networking sites and internet service providers about trolling and ways of identifying those responsible.

"That is the big question and it is one we would wish to explore with internet companies to determine whether they are doing as much as they can or whether they should do more."

He continued: "I think the events of the last few days have shown that actually there does need to be much greater attention paid to this, there needs to be greater urgency.

"I hope that Twitter have seen the strength of public opinion that exists in Britain at the moment and they will be acting swiftly."

More than 88,000 people have so far signed an online petition demanding that Twitter introduce a "report abuse" button urgently on all of its platforms and review its terms and conditions on abusive behaviour.

Twitter says it already has a report button on its iPhone app and plans to roll that out more widely.

Media captionCulture Select Committee Chairman John Whittingdale: "The needs to be greater urgency over doing something about this"

Court cases

But critics argue that does not go far enough and only directs users to the existing reporting form which they say is too long and impractical.

Manually reviewing every tweet is not possible, Twitter argues, due to the site's global reach, but it insists users are required to abide by a code of conduct.

"We value the feedback from our users and are testing ways of simplifying the reporting process, including a broad roll-out of in-tweet reporting beyond the current availability on the iPhone app and mobile web," a spokesman said.

"We have processes in place for working with law enforcement and are currently in communication with the police, as well as the affected parties."

A second female MP, Claire Perry - who has been advising David Cameron on measures to tackle the spread of extreme pornography and child abuse on the internet - has also revealed the abuse she has received on Twitter.

Retweeting a number of offensive messages, she wrote: "I am tempted to shut down my Twitter account given the trolling going on incl. to me - but that would be giving in. #TakeBackTwitter"

Meanwhile, the BBC has learned that more than 1,700 cases involving abusive messages sent online or via text message reached Britain's courts in 2012.

This was a rise of 10% from 2011, according to Crown Prosecution Service figures obtained under a Freedom of Information request.